Biological flourophores are frequently excited with lasers of wavelengths at 488, 514 and 532 nm. The emission wavelength range of biological flourophores may be estimated as 488 to 588 nm.
The cost of chemicals consumed in a biological assay can be significant. Ergo, there is a demand for assays that employ smaller volumes of liquid. However, such smaller volumes can lead to emission signals in the range of 100-1000 photons.
Shot noise describes the statistical error due to a fixed quantum as the square-root of the expected quanta. Unwanted quanta from other image point-spreads might contribute additional shot noise to the signal. A high-contrast optical point-spread is required for the detection of small signals from flourophores. Accordingly, the reduction of shot noise from other object points is essential.
The maximum collection of light dictates a large etendue or space-angle product at the sensor. The dimension of a pixel is defined by the sensor, but typically the angular extent is defined by the lens. The image F-number of the lens should be minimized without contribution to background through increased point-spread. The image F-number IFN is also known as the working F-number WFN. The image F-number represents the half angle of a image ray bundle θIRB at the image and can be determined by the following formula:
  IFN  =            1              2        ⁢        sin        ⁢                                  ⁢                  θ          IRB                      =          WFN      .      
Typically, the F-number of a lens refers an infinitely distant object.
      FN    =          f              D        EnP              ,
Wherein f is the focal length for an infinitely distant object, and DEnP is the diameter of the entrance pupil for an on-axis object. It is important to consider the implication of the F-number of a lens which is defined by an infinity distant object and a magnification of zero. At a magnification of 0.5, the image F-number is at least 1.5 times the F-number.
The image F-number may also increase with field position as indicated by a decreasing relative illumination. In a perfect lens of zero magnification, the relative illumination obeys
            cos      3        ⁢          θ      F        =            cos      3        ⁡          (                        h          F                f            )      
Wherein θF is the field angle and hF is the field height.
Typically, a short focal lens with F2.8 displays a rapid drop in relative illumination with field position. A double Gauss lens requires signification drop of relative illumination. Both of these effects contribute to an image F-number which is much greater than the F-number of the lens. Careful consideration of the image F-number is warranted when photons are scarce. The image F-number of the current invention is a true 2.8 which efficiently matches the telecentric CCD sensors sold under the registered trademark KODAK by the Eastman Kodak Company of Rochester, N.Y.
The object F-number OFN, determines the hemispheircal collection efficiency of point-source or sub-pixel object as
  HCE  =                    1        8            ⁢              1                  OFN          2                      =                  1        8            ⁢                                    M            2                                IFN            2                          .            
The optical length or optical distance is defined as
      Δ    =                  ∑        i            ⁢                        d          i                          n          i                      ,
Wherein di is the spatial length of the i-th material, and ni is refractive index of the i-th material. The optical length represents the equivalent length in air. It should not be confused the optical path length which is related to the number of wavelengths along a path.
The optical power of a surface is defined as
      Φ    =                  n        2                              (                                    n              2                        -                          n              1                                )                ⁢        R              ,
Wherein n1 is refractive index of the first material, n2 is refractive index of the second material, and R is the radius of curvature of the interface of the materials. A radius with origin on the exiting side of the interface is positive, while a radius with origin on the incident side of the interface is negative. The optical power of a doublet is fairly estimated by the sum the optical powers of the three surfaces of the doublet, while the focal length equals the reciprocal of the total power. Ergo the focal length of a doublet is fairly estimated as the reciprocal of the sum of the powers of each surface. An exact expression for summation of the two optical powers Φ12 isΦ12=φ2+φ2−φ1φ2Δ12.
Wherein φ1 and φ2 are the powers of the first and surfaces with an optical length Δ12 between them. As it becomes important later, the power of a meniscus lens is determined by the summation two powers that are similar in magnitude but opposite in sign. Consequently, the power of a meniscus lens decreases as the optical length between the surfaces decreases. The margin of a meniscus lens can have less power the center of a meniscus.
A telecentric orientation of the image rays is highly desirable for sensors with microlens elements for increased quantum efficiency. As the image F-number decreases, telecentric rays at the image become difficult to maintain without aberration. A lower limit of the acceptance F-number for a charge-coupled device (CCD) with a microlens is typically 2.8.
The angular extent of an interline sensor with microlens is displayed in FIGS. 1A and 1B where FIG. 1A displays on-axis rays 45 and FIG. 1B displays the off-axis rays 46. FIGS. 1A and 1B are based upon an interline transfer CCD with microlens (KAI-1020) sold under the registered trademark KODAK by the Eastman Kodak Company of Rochester, N.Y., which employs a transparent dome with square base over each pixel. The transparent dome has a roughly cylindrical profile over a row of active wells 44. Ergo, the transparent dome acts as a microlens 40, which creates an image of a telecentric lens-stop upon an active well 44 at the focal point of the microlens 40. A pixel or picture element comprises an entire active well 44 and two halves of a dark well 48.
FIG. 1A displays a microlens 40 which directs on-axis rays 45 into an active well 44. FIG. 1B displays a microlens 40 which directs off-axis rays 46 into an active well 44. The off-axis rays 46 correspond to the angular limits of an F2.8 image and the sensor. The dark wells 48 provide interline transfer of charge during collection of charge by the active wells 44. The active well 44 does not occupy half of the microlens cell due to shielding by electrical contacts. The microlens 40 effectively directs both on-axis rays 45 and off-axis rays 46 into the active pixel. The microlens 40 can increase the quantum efficiency of a pixel from 9% to 45%. This defines a gain of 5 times in quantum efficiency due to application of a microlens 40 to a telecentric F2.8 image.
Each pixel within the sensor array contains the same distant F2.8 lens-stop. Consequently, the lens-stop of the sensor array is infinitely distant. This condition is known as telecentric which implies “distant center.” The distant lens-stop also defines a distant entrance pupil for the microlens array. Efficient coupling of light by a camera lens into the telecentric sensor requires a distant exit pupil for camera lens that matches the distant entrance pupil of the microlens 40. Placement of the lens-stop within the camera determines the location of the exit pupil of the camera. A telecentric lens is difficult to create at low F-numbers.
Most camera lenses do not provide a distant exit pupil because they are not telecentric at the image. Ergo, the coupling efficiency by camera lens into a CCD with a microlens 40 is not consistent throughout the field. As the field position increases, the F-number decreases due to vignetting by the distant entrance pupil of the microlens 40.
The ability to continue integration during transfer is beneficial to lengthy biological processes that demand faster processes for application to genome sequencing. Shortening the time to process completion is essential to bringing human-genome sequencing to clinical applications.
Contents of N by N pixels may be collected in a larger “bin” through sequencing of electronic gates within a CCD. Binning of N-squared pixels may be employed to achieve an N:1 magnification of the pixel dimension. Binning increases the signal by N-squared while increasing the shot noise by N and maintaining the read noise. Ergo, the signal-to-noise ratio can be increased by N-times until the full-well capacity of the CCD is reached.
If the object becomes a subpixel object or point-source, then only one-quarter of the total signal may be reliably collected by a single pixel. The one-quarter minimum occurs when the image of spot is centered on the shared vertex of four pixels. Ergo, the minimum dimension of the pixel or super-pixel should be half the dimension of the point-source image at the sensor. In one example, a sensor KAI-1020 employs a 7.4 μm by 7.4 μm square pixel with microlens. A 7.5 μm pixel can be chosen for the design, which yields 15 μm as the first super pixel.
The ultimate goal of fluorescent imaging is the collection of enough light from the object to establish high contrast with background and/or noise. Ideally, a low F-number lens should not create large tails because those tails contribute to the background. The spatial extent of the image rays must be localized within the spatial extent of the pixel for minimization of background, while the angular extent of the image rays must be maximized within the angular extent of the pixel for maximum signal strength. The shot noise of the background and the shot noise of the signal cannot be removed from the signal. However, the shot noise of the background can be prevented through careful optical design. A lens with a sharp point spread minimizes background and the associated shot noise.
A consistent spot-size and F-number is paramount in spectroscopy, while the number of pixels, variable focus, zoom, and broad wavelength are not. The full wavelength spectrum of human vision is certainly not required in fluorescent applications, yet many instruments employ camera lenses that were designed for human vision. Furthermore, placement of a plano spectroscopy filter in a low F-number lens creates optical aberrations that reduce contrast and spread edges.
In U.S. Pat. No. 5,831,775, Matsui provides an example of the limitations of an ordinary camera lens. In Matsui '775, Table 3 provides the prescription for a lens with an effective focal length of 105 mm and an F-number of 2.9 at linear magnifications of −0.1, −0.5, and −1.0. The stop is located at surface 7 without further instruction by Matsui '775. Table 3 of Matsui '775 provides data for radius of curvature, thickness, refractive index, and Abbe number for 17 surfaces.
The specifications of a KAI-1020 sensor indicate a relative quantum efficiency of 70% of maximum at 10° from normal incidence 0°. Therefore the angle of acceptance AA of the CCD is defined as 10° for the current discussion. The angle of acceptance of 10° specifies an acceptance F-number of 2.8.
As the lens of Matsui '775 translates from magnifications of −0.1 to −1.0, the lens-stop translates farther from the sensor. Consequently, the image F-number IFN increases steadily. This inflation of IFN with increasing absolute magnification is an undersirable effect in spectroscopy. At magnification of −0.5, the object and image distances are 3f and 1.5f respectively while the IFN becomes 1.5 times the FN. The IFN might increase further if the lens-stop shifts within the lens to improve image quality. As a consequence of F-number inflation, this improved image requires further reduction of collection. With this, the F2.9 lens of Matsui '775 displays an IFN of 4.4 at magnification of −0.5 an IFN of 5.8 at magnification of 1.0. Vignetting may also increase the F-number.
The Matsui '775 lens employs 9 elements with 16 air-to-glass interfaces. The addition of a filter and a cover glass for CCD brings the total to 11 elements with 20 air-to-glass interfaces. Assuming a transmittance of 99% per surface over 21 surfaces, this yields a total transmittance of 82%. Consideration of scatter due to surface imperfections further decreases the transmittance. A lens system with 10 air-to-glass interfaces of 99% transmittance would display a transmittance of 90% with less scatter. The large number of surfaces in Matsui '775 permits a large range of magnification which is not required in fluorescent spectroscopy.
Vignetting results from a clipping of rays from off-axis objects for management of aberrations throughout the entire image. The word vignette implies use of vines to soften edges within architecture. Such softening of edges can hide astigmatism and coma within the margin of the field. Vignetting is not desirable in spectroscopy where collection efficiency and point-spread must be maintained throughout the field. Vignetting might be pleasing to the eye in photography, but the associated reduction in photon count is detrimental to low-light spectroscopy. Vignetting must be eliminated or at least minimized, as the performance of the instrument is limited to the point of weakest irradiance and/or contrast within the image. Many lenses employ vignetting for maintenance of point-spread. There is also another source of vignetting besides clipping. The solid angle of the lens-stop with respect to the object point displays a cosine-cubed dependency upon field angle. This particular type of vignetting can be minimized through minimization of field angle. Consequently, a wide angular field is detrimental in spectroscopy. However, a narrow angular field requires a longer lens, which is not beneficial to photography by humans, but is acceptable for machine vision.
Back-illuminated CCDs, such as the iXon DU-898 BI by Andor Technology of Belfast, Northern Ireland, can display a quantum efficiency of 90% without a microlens array. However, back-illuminated CCDs are extremely difficult to manufacture, and, consequently, are much more expensive than front-illuminated CCDs with microlens arrays. Furthermore, back-illuminated CCDs are not immune to the intrinsic vignetting of an ordinary camera lens. Consequently, an F2.8 lens without vignetting is still advantageous for back-illuminated CCDs.
In light of the foregoing, it will be appreciated that there exists a plurality of deficiencies in the current lens technology for the efficient collection of fluorescent signals from biological assays. The application of single molecule detection demands higher collection efficiency, less background noise, and less vignetting. A lens with a telecentric image for application to CCDs with microlens elements is highly advantageous.
There are two lens types in the prior art with similar structure to the current invention: a Petzval lens, and a tube lens. The Petzval Lens was conceived in 1840 with numerous variations to follow. The tube lens is a development late 1900s for infinity-corrected objective lenses with microscope structures. More description of these lenses in relation to the current is presented as follows.
A Petzval lens comprises a first and second doublet wherein the second doublet is midway between the first doublet and the sensor. The Petzval lens displays significant Petzval curvature which describes the defocus of the image across the sensor. A negative field flatter may be placed near the sensor to correct for this curvature. The rays of the margin substantially overlap the rays of center in the first group. The rays of the margin are substantially separated from the rays of center in second group. The concept is similar to the goal of the current invention without application of the specific features of the invention, wherein a positive meniscus of the second group achieves field-flattening though increased optical distance at the margin of the second group.
A tube lens by Nikon displays similar shape to the current invention in U.S. Pat. No. 5,699,196 to Misiwa. It comprises a positive doublet as the first group and a negative meniscus as the second lens as defined in FIG. 3 and Table 1 of Misiwa U.S. Pat. No. 5,699,196. Application of the prescription tube lens in Table 1 reveals that the second group is negative meniscus. Given a 10 mm entrance pupil and 200 mm effective focal length, the operating F-number is 20 for the tube lens. The rays of the margin are substantially separated from the rays of center in both groups.
The concepts of the Petzval lens and the Misiwa tube lens are similar to the goal of the current invention, but very different from the specific features of the invention. The Petzval lens and the Misiwa tube lens both separate rays of margins from rays of center within the second group. However, neither the Petzval lens nor the Misiwa tube lens employ a positive meniscus lens for field-flattening though increased optical distance at the margin of the second group. They both employ a negative element as a field flattener.